Question

Two spherical rain drops with radii in the ratio $1:2$ fall from a great height through the atmosphere. The ratio of their momenta after they have attained terminal velocity is

• A. 1 : 8
• B. 2 : 1
• C. 1 : 32
• D. 1 : 2
• E. 1 : 16

Answer 1

Answer: (C)

1 : 32

Given, $r_1:r_2=1:2$
We know that,
$v\propto r^3$ and $m\propto r^3$
$\frac{v_1}{v_2}={\left(\begin{array}{c}\frac{r_1}{r_2}\end{array}\right)}^3$ and $\frac{m_1}{m_2}={\left(\begin{array}{c}\frac{r_1}{r_2}\end{array}\right)}^3$
We also know that momentum
$p\propto mv$
Hence, $\frac{p_1}{p_2}=\frac{m_1{v}_1}{m_2{v}_2}={\left(\begin{array}{c}\frac{r_1}{r_2}\end{array}\right)}^5$
$\frac{p_1}{p_2}={\left(\begin{array}{c}\frac{1}{2}\end{array}\right)}^5$
$p_1:p_2=1:32$